Question

A sphere and a cone have the same volume, and each has a radius of 6 centimeters. What is the height of the cone?

Solid Geometry
ANSWERED
asked 2021-02-21
A sphere and a cone have the same volume, and each has a radius of 6 centimeters. What is the height of the cone?

Answers (1)

2021-02-22

Equate the volumes of the sphere and the cone: Vsphere=Vcone \(\displaystyle\frac{{4}}{{3}}π{r}^{{3}}=\frac{{1}}{{3}}π{r}^{{3}}\)
Substitute r=6 cm and solve for h:
\(\displaystyle\frac{{4}}{{3}}π{\left({6}\right)}^{{3}}=\frac{{1}}{{3}}π{\left({6}\right)}^{{2}}{h}\)
\(\displaystyle{288}π={12}π{h}\)

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